Prime Factorization Calculator
Find the prime factorization of any integer — the unique way to express it as a product of prime numbers.
How to use the Prime Factorization Calculator
- Enter your inputs into the Prime Factorization Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The prime factorization process
Trial-divide n by primes 2, 3, 5, 7, ... up to √n; collect factors with their multiplicities
Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). Trial division is simple but slow for very large numbers; faster methods exist (Pollard rho, etc.).
Worked example
360 = 2 × 180 = 2 × 2 × 90 = 2³ × 45 = 2³ × 3² × 5. Prime factorization: 2³ × 3² × 5. 1,000 = 2³ × 5³. 17 is prime: 17¹.
Frequently asked questions
Why is prime factorization unique?
The Fundamental Theorem of Arithmetic guarantees that every integer above 1 has exactly one prime factorization, up to the order of factors. This uniqueness underlies much of number theory.
What's the largest known prime?
As of recent records, Mersenne primes like 2^82,589,933 − 1 (over 24 million digits) are the largest known primes. New ones are found through the GIMPS distributed computing project.
How is this used in cryptography?
RSA encryption relies on the difficulty of factoring the product of two large primes. A 2048-bit RSA key takes centuries to factor with current methods — that's the security guarantee.